Iterative solvers in implicit time integration for compressible flows [Elektronische Ressource] / vorgelegt von Bernhard Pollul

Iterative Solvers in Implicit TimeIntegration for Compressible FlowsVon der Fakultat¨ fur¨ Mathematik, Informatik und Naturwissenschaftender RWTH Aachen University zur Erlangung des akademischen Gradeseines Doktors der Naturwissenschaften genehmigte Dissertationvorgelegt vonDiplom-MathematikerBernhard Pollulaus BonnBerichter: Universit¨atsprofessor Dr. Arnold ReuskenUniversit¨ atsprofessor Dr. Marek BehrTag der mundlic¨ hen Prufung:¨ 05. November 2008Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfugbar.¨Contents1 Introduction 11.1 Motivation.................................... 11.2 The Adaptive Finite Volume Solver QUADFLOW ..... 21.3 Outline of the Main Results ...... 31.4 Overview of the Contents................. 72 Description of Motion for Inviscid Compressible Gas 112.1 The Euler Equations .............................. 12.2 Domains, Initial and Boundary Conditions ......... 132.3 First Example .............. 143 The QUADFLOW Solver 173.1 Features of QUADFLOW ........................... 173.2 Grid Generation............. 203.2.1 Nested Grid Hierarchy ..... 203.2.2 Parametric Meshes ................ 213.2.3 B-Spline Representation ............... 223.2.4 Multi-block Concept ...... 233.3 Flow Solver ........................ 233.3.1 Finite Volume Discretization.. 243.3.2 Upwind Methods ................... 253.3.3 Time Discretization................ 263.3.3.1 Implicit Time Integration Schemes .... 263.3.